I personally would try and go for a match here. Not because it would give Edward and Louis and alliance, but also because their mother,
Margaret II, Countess of Hainault (1311–1356), is the older sister of Philippa, meaning the arranged marriage could be done through them.
Elisabeth of Bavaria (1329 – 2 August 1402) married in 1350, so if they could marry before, or her first died in 1359. IOTL she had 9 sons (not all live to adulthood) but either way this will be very interesting to see how more branches of the Plantagenet family can form with alternative roses sprouting up to rival those of York and Lancaster.
The problem you may find with Agnes of Bavaria (1335 – 11 November 1352) unless the P.o.D. Is that she is born health is that IOTL, she rejected a marriage with a nobleman chosen by her relatives and instead entered a cloister, as she was a sickly person for most of her short life and died in 1352 aged 17.
As well as the two ladies above their older sister, Anna of Bavaria, Dowager Duchess of Lower Bavaria (c. 1326 – 3 June 1361) although four years older then Edward, is widowed without issues, in 1340 so could be offered as well.
The only problem we may have is in regards to the dispensation that is needed to be obtained for their marriage due to closeness of relation, may be denied by Pope Clement VI, whom is not on best terms with either Edward III, (for refusing a summoning in 1328 and encroachments on ecclesiastical jurisdiction) or Louis IV, Holy Roman Emperor (having excommunicated the Emperor, and directed the election of Charles IV, in 1346)
I would choose Elizabeth and marry her to Edward in a proxy wedding in 1349 and her travel to England to marry in person before his return to France is 1355.
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Edward of Woodstock, “the Black Prince” (15/6/1330–8/6/1376) m.
By Proxy. 1349,
In Person. 1351, Elisabeth of Bavaria (c. 1329–2/8/1402)
1) Edward of Chester (1353–1410) [1] m.
2) Richard of Winchelsea, Duke of Cambridge (1355–1404) [2] m. 1371, Constance of Castile (1354–1394) [see 8]
3) Louis of Bordeaux (1357–1372) [3]
4) William of London (1359–1375) [4]
5) Henry of La Rochelle (1362-1412) [5] m.
6) Peter of Angoulême (1363-1403) [6] m. 1375, Eleanor de Bohun, Countess of Hereford and Essex (c. 1366 – 3 October 1399)
7) Lionel of Angoulême (1365-1370) [7]
8) Alphonso of Capbreton (1366-1413) [8] m.
9) Thomas of Bordeaux (1367 –1422) [9] m.
[1] In 1353 some disturbances seem to have broken out in
Cheshire, for the Prince as
Earl of Chester marched with Henry of Grosmont,
Duke of Lancaster to the neighbourhood of
Chester to protect the justices, who were holding an assize there. Pregnant Elizabeth travelled with them and would give birth within their lodgings in Chester.
[2] Richard was born just before his parents departed Winchelsea to campaign in France, Richard along with his older brother, would stay in England with the governesses and household.
[3] Named after his maternal grandfather, Louis IV, Holy Roman Emperor, whom had died 10 years previously) as well as his maternal uncles, Louis V, Duke of Bavaria and Louis the Roman, whom stood as god parents.
[4] Born a few month before his father, left with his grandfather, during the Reims campaign. He was named after his fathers younger brother, whom died within a year of his birth as well as his ancestor, William the Conqueror.
[5] Henry was born during the journey between England and Gascony, as his family landed in La Rochelle, the prince was greeted with cheers and applause.
[6] Born around May 1363, when his father entertained Peter, King of Cyprus at Angoulême, and named his son in his honour.
Peter would be married to Eleanor de Bohun the elder daughter and co-heiress (with her sister, Mary de Bohun), of Humphrey de Bohun, 7th Earl of Hereford (1341–1373), by his wife Joan Fitzalan, a daughter of Richard FitzAlan, 10th Earl of Arundel and his second wife Eleanor of Lancaster. Eleanor and her husband had the tutelage of her younger sister, Mary, who was being instructed in religious doctrine in the hope that she would enter a convent, thus leaving her share of the considerable Bohun inheritance to Eleanor and Peter.
[7] Born in at Angoulême, and named after his uncle, Lionel, Duke of Clarence. He would sadly die of the bubonic plague before his 5th birthday.
[8] Born in the town of Capbreton, where is mother and father, had been waiting to greet King Peter of Castile to flee from his kingdom with his son and his three daughters, it was during this meeting that Edward would arrange the marriage of his second son, to the eldest daugter, Constance of Castile. He was named in honour of both Alphonso, Earl of Chester and Peter's son, Alfonso, Prince of Asturias.
[9] Born during the Spanish Campaign of 1365-67, Edward, the Black Prince stayed over Christmas at Bordeaux, where Princess Elizabeth, gave birth to their final son.
